Help with this derivative?

It is from the infinite series section of the book, but I must have missed class this day because I don't know how to solve it. I don't need it worked out, just a point in the right direction. The problem is to compute the 7th derivative of

I know he doesn't expect us to manually take the derivative 7 times, so what is the trick?

Thank you, but I understand how to manually compute the 7th derivative with the product rule. This is not what I am being tested on. It has something to do with series, but I can't find another example like this in my notes.